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Pondering Productivity

(a) Is either farm more productive than the other in eggs per hen per day?
(b) Smith has 48 hens. How long must he wait to first get a whole number of eggs at the close of a day? How many eggs does his farm produce in that time?
(c) Jones has 300 hens. How many days must he wait to first get a whole number of eggs at the close of a day? How many eggs does his farm produce in that time?

Cornfield Planning

A farmer has a square plot of land that measures 100 feet on each side. She plans to grow corn in the plot, and she will install a fence around the corn. Fencing is expensive, so she wants to grow the corn in a shape that will maximize the ratio of the area of the cornfield to its perimeter.

Solutions to week 138

Close to a Quart answer explained:
By transferring water n = 2(a + b – 1) times, you can achieve water in one of the two containers in the amount of ae – bπ or aπ – be, making sure the expression used is positive. You must find the smallest integer value of a + b so that.99 < ae – bπ < 1.01 or .99 < aπ - be < 1.01. By numerical search, you find 73π - 84e = 1.00059 and 57e – 49π = 1.004024 are the smallest values satisfying the above conditions. Thus a = 57 and b = 49 gives n = 210 as the minimum number of transfers.

Math Party answer explained:
The children are 4, 4, and 9 so their sum is 17 and their product is 144. Smith incorrectly guessed (3, 6, 8) for the ages. One year ago, the ages were (3, 3, 8) and Jones incorrectly guessed (2, 6, 6).